find the domain of the following functions
f(x)=1/x+ 5/x-3
I will assume you mean
f(x) = 1/x + 5/(x-3)
the domain would be the set of all real numbers, except x=0 and x=3
yes
so how do you write the domain as a equation
domain:
x all real except x=0 and x=3
To find the domain of a function, we need to identify all the values of x for which the function is defined.
For the function f(x) = 1/x + 5/x - 3, we need to determine any values of x that would make the denominator equal to zero, since division by zero is undefined.
First, let's look at the denominator of the first term, 1/x. The denominator, x, cannot be zero, so x ≠ 0.
Then, let's examine the denominator of the second term, 5/x. Again, the denominator, x, cannot be zero, so x ≠ 0.
Finally, consider the denominator of the third term, x - 3. Setting this equal to zero and solving for x, we get x = 3. Therefore, x ≠ 3.
Combining these restrictions, the domain of the function f(x) = 1/x + 5/x - 3 is all real numbers except for x = 0 and x = 3.
In interval notation, the domain can be written as (-∞, 0) U (0, 3) U (3, ∞).